{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Calculus_with_Python1.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyONR7niwo8Xto2Vd58ErdfA",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/Divyanshu-ISM/Oil-and-Gas-data-analysis/blob/master/Calculus_with_Python1.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NLGZ6TldL8Tw",
        "colab_type": "text"
      },
      "source": [
        "#Chapter 1: Solving ODEs"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "u-XGpTNrLx-U",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "from scipy.integrate import odeint\n",
        "\n",
        "%matplotlib inline"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iNAaWZ2GMRUp",
        "colab_type": "text"
      },
      "source": [
        "#Problem 1. \n",
        "\n",
        "$ \\frac {dy} {dx} = -ky$\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "etCghE3EMJDe",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#1. Model creation\n",
        "\n",
        "def model(y,x):\n",
        "  k = 0.5\n",
        "  dydx = -k*y\n",
        "  return dydx\n",
        "\n",
        "#2. x \n",
        "x = np.linspace(0,10,20)\n",
        "\n",
        "# 3. Intital value\n",
        "y0 = 5\n",
        "\n",
        "#solution\n",
        "y = odeint(model,y0,x)"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "69txj8DFPXlR",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "dcb66432-4066-4bdd-e143-cb9653f82b08"
      },
      "source": [
        "plt.plot(x,y)"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f3bfaddb1d0>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-xcr2yRRQDcE",
        "colab_type": "text"
      },
      "source": [
        "#Problem 2. \n",
        "\n",
        "$5\\frac {dy(t)}{dt} = -y(t) + u(t) $"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9gE21EwQPd2U",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "4c717fa2-de52-49e8-970b-eadc2ee0e4df"
      },
      "source": [
        "def model(y,t):\n",
        "  if t<=10:\n",
        "    u = 0\n",
        "  else:\n",
        "    u = 10\n",
        "  dydt = (-y + u)/5.0\n",
        "  return dydt\n",
        "\n",
        "t = np.linspace(0,100,100)\n",
        "\n",
        "y0 = 10\n",
        "\n",
        "y = odeint(model,y0,t)\n",
        "\n",
        "plt.plot(t,y)\n",
        "\n",
        "\n"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f3bfad30198>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3MCikz32RUMu",
        "colab_type": "text"
      },
      "source": [
        "#The Soul concept : isolate the derivative on the LHS | everything else RHS"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tFJPTLPRQ2tN",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#######"
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OFe3ZRfkRryS",
        "colab_type": "text"
      },
      "source": [
        "#Problem 3. Two ODEs together. \n",
        "\n",
        "$\\frac{dx(t)}{dt} = - 3exp(-t)$\n",
        "\n",
        "$\\frac{dy(t)}{dt} = 3 - y(t)$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "clNxbHeORqB9",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#the outputs of x and y will be stored in a two sized array. \n",
        "\n",
        "def modell(z,t):\n",
        "  x = z[0]\n",
        "  y = z[1]\n",
        "  dxdt = 3.0*np.exp(-t)\n",
        "  dydt = 3.0 - y\n",
        "  return [dxdt,dydt]\n",
        "\n",
        "z0 = [0,0]\n",
        "\n",
        "t = np.linspace(0,10)\n",
        "\n",
        "z = odeint(modell,z0,t)"
      ],
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LikhMrH9Wl9p",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# print(z) #hence z is a 2D array"
      ],
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Vk44oqwCV_uO",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "106c1e49-7453-4898-a317-13b56fe73cc7"
      },
      "source": [
        "plt.plot(t,z[:,0],label = 'Solution for x(t)')\n",
        "plt.plot(t,z[:,1],label = 'Solution for y(t)')\n",
        "\n",
        "plt.legend()\n"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f3bfaae3400>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 20
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LnFmYKs5Wb3K",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}